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Cauchy problem with general discontinuous initial data along a smooth curve for 2-d Euler system. (English) Zbl 1302.35239
The authors consider the Cauchy problem for the isentropic Euler system in two spatial dimensions. The initial data are smooth at both sides of a smooth curve, but are discontinuous on this curve. Local existence of a piecewise smooth solution is proven. The solution contains three kids of singularities: shock wave, rarefaction wave, and contact discontinuity. The proof is based on an accompanying one-dimensional Riemann problem.

35L60 First-order nonlinear hyperbolic equations
35L65 Hyperbolic conservation laws
35L67 Shocks and singularities for hyperbolic equations
76L05 Shock waves and blast waves in fluid mechanics
35R05 PDEs with low regular coefficients and/or low regular data
35Q31 Euler equations
Full Text: DOI
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